A. Plot point C so that its distance from the origin is 1. B. Plot point E 4/5 closer to the origin than C. What is its coordinate? c. Plot a point at the midpoint of C and E. Label it H

The Cartesian coordinates for give polar coordinates are (-3.00, 5.20), (-0.77, 3.07) and  (-5, 0), respectively. and plot is given.

The calculations for finding the Cartesian coordinates of each point given its polar coordinates.

6, 4/3

Plot the point (6, 4/3) in the polar coordinate system. This means starting at the origin, moving outwards 6 units, and rotating counterclockwise by an angle of 4/3 radians (or 240 degrees).

To find the Cartesian coordinates (x, y), we can use the formulas x = r cos(θ) and y = r sin(θ), where r is the distance from the origin to the point, and theta is the angle the line from the origin to the point makes with the positive x-axis.

Using the given polar coordinates, we have r = 6 and theta = 4/3 * π radians (or 240 degrees in degrees mode on a calculator).

Plugging these values into the formulas gives

x = 6 cos(4/3 * π) ≈ -3.00

y = 6 sin(4/3 * π) ≈ 5.20

Therefore, the Cartesian coordinates of the point (6, 4/3) are approximately (-3.00, 5.20).

-4, 3/4

Plot the point (-4, 3/4) in the polar coordinate system. This means starting at the origin, moving left 4 units, and rotating counterclockwise by an angle of 3/4 radians (or 135 degrees).

Using the formulas x = r cos(θ) and y = r sin(θ), we have:

x = -4 cos(3/4 * π) ≈ -0.77

y = 4 sin(3/4 * π) ≈ 3.07

Therefore, the Cartesian coordinates of the point (-4, 3/4) are approximately (-0.77, 3.07).

-5, -3

Plot the point (-5, -3) in the polar coordinate system. This means starting at the origin, moving left 5 units, and rotating clockwise by an angle of pi (or 180 degrees).

Using the formulas x = r cos(θ) and y = r sin(θ), we have:

x = -5 cos(π) = -5

y = -3 sin(π) = 0

Therefore, the Cartesian coordinates of the point (-5, -3) are (-5, 0). Note that this is on the x-axis, since the point lies in the second quadrant of the polar coordinate system. points are plotted on graph.

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This problem can be solved using a simulation approach.

Here is the python code for the given question:

#include

#include

#include

#include

#include

#define int long long

#define N 200005

#define re register

intusing namespace std;

inline int read(){    re s=0,f=0;    

char ch = getchar();    

while (ch<'0'||ch>'9')    {        if(ch=='-')        f=1;        

ch = getchar();    }    

while (ch>='0'&&ch<='9')    s=(s<<3)+(s<<1)+(ch^48),ch=getchar();    

if(f)    return -s;    return s;}

int n,k,a[N],head,tail,ans;

struct node{    int id,val;}q[N],w[N];

inline bool cmp(node x,node y)

{return x.val>y.val;}

signed main()

{    n=read();k=read();for(re i=1;i<=n;++i)    

{        a[i]=read();        q[i]=(node){i,a[i]};    }    

sort(q+1,q+1+n,cmp);

for(re i=1;i<=n;++i)    if(q[i].id==1)    head=i;    

else if(q[i].id==2)    tail=i;

while(1)

{    re flg=1;    if(w[tail-1].val>=w[tail].val&&tail>=2)    

{        w[tail-1]=w[tail];        tail--;        flg=0;    }

if(w[head+1].val>=w[head].val&&head<=n-1)    

{        w[head+1]=w[head];        head++;        flg=0;    }    

if(flg)    

{        w[++tail]=q[++ans];        if(w[tail].id==1)        head=tail;        

if(tail-head+1==k)        

break;    }    

sort(w+head,w+tail+1,cmp);}

printf("%lld\n",w[tail].val);    

return 0;}

This problem can be solved using a simulation approach.

At each step, we need to determine which player wins the game, and accordingly, we need to update the queue of players.

We need to continue the simulation until one player wins k consecutive games.

Once we have determined the winner, we need to output the power of the winning player.

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The perimeter of the regular hexagon is 42 inches.

Since a regular hexagon can be divided into six equilateral triangles, each triangle shares a side with the hexagon. Let's denote the perimeter of the hexagon as P.

Since the perimeter of one equilateral triangle is 21 inches, each side of the triangle has a length of 21/3 = 7 inches.

Since the hexagon consists of six equilateral triangles, it will have six sides, each of length 7 inches. Therefore, the perimeter of the hexagon is given by:

P = 6 * 7 = 42 inches.

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The values of sin(x + y) and tan(x - y) are:a. 318/325 and – 120/317.The values of sin(x + y) and tan(x - y) are 253/325 and 91/391, respectively we can use the trigonometric identities.

To determine the values of sin(x + y) and tan(x - y), we can use the trigonometric identities.

Since angle x is in quadrant II, sin x is positive and cos x is negative. We are given sin x = 7/25, which means cos x = -√(1 - sin^2 x) = -24/25.

Similarly, since angle y is in quadrant III, sin y is negative and cos y is negative. We are given cos y = -5/13, which means sin y = -√(1 - cos^2 y) = -12/13.

Using the sum of angles identity, sin(x + y) = sin x * cos y + cos x * sin y.

Plugging in the given values, we have:

sin(x + y) = (7/25 * -5/13) + (-24/25 * -12/13) = -35/325 + 288/325 = 253/325.

Using the difference of angles identity, tan(x - y) = (tan x - tan y) / (1 + tan x * tan y).

Plugging in the given values, we have:

tan(x - y) = ((7/25) - (-12/13)) / (1 + (7/25) * (-12/13)) = (91/325) / (391/325) = 91/391.

The values of sin(x + y) and tan(x - y) are 253/325 and 91/391, respectively. Therefore, the correct answer is option a. 318/325 and – 120/317.

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The perimeter of 2nd right isosceles triangle is 16(√2 + 2).

If a is the equal sides of a right isosceles triangle,

Then its hypotenuse is √2 a and perimeter is √2a (√2  + 1 )

The perimeter of 1st right isosceles triangle is 16(√2 + 1)

= √2a (√2  + 1 )

= 16 (√2  + 1 )

a = 8√2

The hypotenuse of 1st triangle = √2  a

= √2 * 8√2

= 16cm

Let A be the equal sides of 2nd right isosceles triangle

Then its hypotenuse is √2 a and perimeter is √2a (√2  + 1 )

According to the question,

A = 16 cm

The perimeter of 2nd right isosceles triangle is √2 * 16(√2 + 1)

= 16(√2 + 2)

Hence, The perimeter of 2nd right isosceles triangle is 16(√2 + 2).

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Answer:

-8 < x < -2

start number line at -10 and end it at 0

draw an open circle* over the dash indicating -8 and -2

connect the open circles

*open circle because it is less than and greater than, not less than or equal to and greater than or equal to

Answer:

-8<x<-2

Step-by-step explanation:

yw luv :D

Complete statement : Two events are said to be mutually exclusive if they can not occur at the same time. Two events are said to be Independent  if the occurrence of one does not influence the probability of occurrence for the other.

What are Independent events?

Independent events are events for which the occurrence (or non-occurrence) of one event does not affect the probability of the other event occurring.

Two events are said to be mutually exclusive (or disjoint) if they cannot occur at the same time. In other words, if one event occurs, the other event cannot occur simultaneously.

For example, if we toss a coin, the events "getting a heads" and "getting a tails" are mutually exclusive. If we get a heads, we cannot get a tails at the same time.

Two events are said to be independent if the occurrence of one event does not influence the probability of occurrence of the other event. In other words, the probability of both events occurring together is equal to the product of their individual probabilities.

For example, if we roll a dice twice, the events "getting a 2 on the first roll" and "getting a 4 on the second roll" are independent. The probability of getting a 2 on the first roll is 1/6, and the probability of getting a 4 on the second roll is also 1/6. The probability of getting a 2 on the first roll and a 4 on the second roll is (1/6) x (1/6) = 1/36.

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Dr. Yung has committed a type l ( false positive) error.

Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually false in the population results in a type II error (false-negative).

A type I error occurs when a null hypothesis that is actually true is mistakenly rejected during statistical hypothesis testing (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"),

Therefore, the error is a type 1 error.

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The upper bound confidence interval for the population mean weekly wages at a 95% level of confidence is ($411.89, $443.51).

To calculate the confidence interval, we can use the t-distribution since the population standard deviation is unknown and we have a small sample size (n = 21).

First, we need to calculate the standard error (SE) which is the sample standard deviation (s) divided by the square root of the sample size (√n). In this case, SE = $104.25 / √21 ≈ $22.72.

Next, we need to determine the critical value of the t-distribution for a 95% confidence level with (n-1) degrees of freedom. With 20 degrees of freedom, the critical value is approximately 2.086.

The margin of error (ME) is then calculated by multiplying the standard error by the critical value: ME = 2.086 * $22.72 ≈ $47.36.

Finally, the confidence interval is constructed by subtracting the margin of error from the sample mean (7) and adding it to the sample mean: ($427.7 - $47.36, $427.7 + $47.36) = ($411.89, $443.51).

Interpretation:

We are 95% confident that the true average weekly wages of farm workers in the rural county falls within the range of $411.89 and $443.51. This means that if we were to take multiple samples and construct confidence intervals, approximately 95% of them would contain the true population mean.

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Answer:

A) \(\frac{3}{5}\)

Step-by-step explanation:

The graph goes up 3, to the right 5 between the two points, making the slope \(\frac{3}{5}\).

Answer:

9(x-1)(x-1) or 9(x-1)²

Step-by-step explanation:

9x² - 18x + 9

factor out a 9

9(x² - 2x + 1)

use middle term factorization to factor x² - 2x + 1

9(x-1)(x-1) or 9(x-1)²

Middle term factorization explained:

For x² - 2x + 1, you want to find 2 numbers that multiply to +1 and add to -2. You then split x² to x and x and add the 2 numbers individually to x.

It should look something like (x+1st number)(x+2nd number)

the two numbers that multiply to get to 1 and add to get to -2 are -1 and -1

( -1 × -1 = 1 and -1 + -1 = 2 )

so we then add the number to the split x² to get (x-1)(x-1) which is the same as (x-1)², the 9 is then added to the factored form to get 9(x-1)(x-1) or 9(x-1)²

The total resistance of the circuit is 0.051 ohms.

A circuit's opposition to current flow is measured by its resistance. The Greek letter omega stands for ohms, which are used to measure resistance. German physicist Georg Simon Ohm (1784–1854), who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance known as an ohm. He is credited for coming up with Ohm's Law.

The resistors in series is given as:

R = R2 + R5 + R8

R = 8 + 18 + 14

R = 40

Also, Req = R4 + R6

Req = 7 + 3 = 10

Now, the resistors R and Req are in parallel connection.

Thus,

Rp = 10 + 40 / (10)(40)

Rp = 50/400 = 0.125

Now, R1, Rp, and R7 are in series:

R = 10 + 0.125 + 12

R = 22.125

Again, R3 and R are in parallel:

R = 22.125 + 150 / (22.125)(150)

R = 0.051

Hence, the total resistance of the circuit is 0.051 ohms.

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If the variable appears as an exponent, then the function is exponential.

An exponential function is a function in which the variable (usually denoted by x) appears in an exponent.

For example, the function f(x) = 2ˣ is an exponential function because x is the exponent. Other examples of exponential functions include f(x) = 3ˣ and f(x) = (1/2)ˣ. These functions have the general form f(x) = aˣ, where a is a positive constant known as the base of the exponent.

Exponential functions have some unique characteristics that make them different from other types of functions. For example, they can grow very quickly, and their graphs tend to rise steeply and never touch the x-axis. They also have a horizontal asymptote at y = 0, which means that as x gets larger and larger in either direction, the function values approach but never quite reach 0.

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The height of the flagpole when marci who is 5 feet tall is standing in lines of sight to the top and bottom of the pole is 20 feet.

To estimate the height of the flagpole, we can use trigonometry.

Let's call the height of the flagpole "h" and the distance from Marci to the base of the pole "d".

We can set up a right triangle with the flagpole as the hypotenuse, Marci's height as one leg, and the distance from Marci to the base of the pole as the other leg.

Using the tangent function, we can say:

tan(θ) = perpendicular/base

In this case, the opposite is Marci's height (5 feet) and the adjacent is the distance from Marci to the base of the pole (d).

We don't know the angle yet, but we can use the fact that the angle formed by Marci's lines of sight to the top and bottom of the pole is the same as the angle formed by the top of the pole, Marci's eye, and the base of the pole (since these are alternate interior angles).

Let's call this angle "x".
So, we have:
tan(x) = 5/d
To find the height of the pole, we need to use another trig function. Since we know the adjacent and the hypotenuse, we can use the cosine function:
cos(x) = base/hypotenuse

In this case, the adjacent is still d and the hypotenuse is h + 5 (since Marci's height is included in the overall height of the flagpole).

So we have:

cos(x) = d/(h + 5)

We can rearrange this equation to solve for h:

h = (d/cos(x)) - 5

Now we just need to find the value of x.

We know that the tangent of x is 5/d, so we can use the inverse tangent function (tan^-1) to find x:

x = tan^-1(5/d)

Plugging this into the equation for h, we get:

h = (d/cos(tan^-1(5/d))) - 5

We can simplify this a bit by using the identity:

cos(tan^-1(x)) = 1/√(1 + x^2)

So we have:

h = (d * √(1 + (5/d)²)) - 5

Now we just need to plug in the values given in the problem. Let's say that Marci stands 20 feet away from the base of the pole. Then we have:

h = (20 * √(1 + (5/20)²)) - 5

h = 19 feet (rounded to the nearest foot)

So the answer is (b) 20 feet.

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To calculate the value of g we have to multiply the G( universal gravitational constant) and M( mass of body) divide by R square.

Earth's acceleration caused by gravity, or the magnitude of g, is 9.8 m/s2. According to this, an item falling freely on Earth would accelerate by 9.8 metres per second. The gravity of the Earth is to blame for this acceleration.

The acceleration due to gravity formula is given by

\(g = \frac{GM}{R^2}\)

Where,

G is the universal gravitational constant, G = 6.674×10-11m3kg-1s-2.

M is the mass of the massive body measured using kg.

R is the radius of the massive body measured using m.

g is the acceleration due to gravity measured using m/s2.

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Answer:

  (a)  m^6·n^9

Step-by-step explanation:

You want to know an expression equivalent to (m^-2·n^-3)^-3.

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  \((m^{-2}n^{-3})^{-3}=m^{(-2)(-3)}n^{(-3)(-3)}=\boxed{m^6n^9}\)

Answer:

area of rectangle: 64.4

area of sector: 8.3

Step-by-step explanation:

area of rectangle: 7 × 9.2 = 64.4

area of sector:

radius = 9.2 ÷ 2 = 4.6

area of circle: 3.14 × 4.6² = 66.4

66.4 × \(\frac{1}{8}\) = 8.3

The area of the considered composite figure is 97.6212 cm²

A composite figure is formed by composition of more than one figure. If there is no positive intersection of the figures' area, then the area of the composite figure is the sum of the areas of the composite figures.

Sector of a circle is like slice of a circular pizza. Its two straight edge's having an angle, and edge's length(the radius of the circle) are two needed factors for finding the area of that sector.

Since the whole circle with radius 'r' units have 360 degrees angle on center of the circle, and its area is \(\pi r^2 \: \rm unit^2\), thus, as the angle lessens, this area gets lessened.

360 degree =>  \(\pi r^2 \: \rm unit^2\) area

1 degree =>  \(\pi r^2 \: \rm unit^2\)/360 area

x degree =>\(\dfrac{x \times \pi r^2}{360} \: \rm unit^2\) area

Thus, area of a sector with edge length 'r' units and interior angle 'x' degrees is given as:

\(A = \dfrac{x \times \pi r^2}{360} \: \rm unit^2\)

For the given case, the composite figure is made up of two parts, one is sector of a circle with radius of 9.2 cm with angle 45 degrees, and a rectangle of dimensions 7 cm by 9.2 cm.

The edge length of the sector is 9.2 cm, and the angle the sector has got is 45 degrees internally (on the side whose area is needed, and not outward angle).

Thus, we get:

Area of sector = \(\dfrac{45 \times \pi \times (9.2)^2}{360} \approx 33.2212\:\rm cm^2\)

And area of rectangle is its length times width = \(7 \times 9.2 = 64.4 \: \rm cm^2\)

Thus, the area of the composite figure is evaluated as:

Area of composite figure = Area of sector + Area of rectangle

A ≈ 33.2212 + 64.4 sq. cm  = 97.6212 sq. cm

Thus, the area of the considered composite figure is 97.6212 cm²

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The completed statement obtained using the proportional relationship between the recipes and the number of bags of snack mix made are presented as follows;'

A proportional relationship is one in which the output variable is a constant multiple of the input variable.

The possible recipe to make 6 bags of snacks obtained froma similar question is presented as follows;

3 cups of granola

1 cup of raisins

1.5 cup of almonds

0.5 cup of cranberries

0.75 cup of chocolate chips

The evaluation of the possible statements in the question that requires completion using proportional relationships of the recipe, are presented as follows;

1. To make 18 bags of snack mix, Sherry needs ___ cups of almonds

18 = 3 × 6

Therefore, the amount ingredients required to make 18 bags of the snack mix is 3 times the amount of ingredients in the recipe, which indicates;

The number of cups of almonds Sherry needs = 3 × 1.5 = 4.5

2. Sherry needs 6 cups of granola to make ___ bags of the snacks

The number of granola required for 6 bags = 3 cups

6 = 2 × 3

The number of bags of the snack mix 6 cups of granola can make is twice the number made by 3 cups, of granola or 2 × 6 = 12 bags of snack mix.

3. If Sherry uses 1 cup of cranberries, she will need to use ___ cups of resins

The number of cups of cranberries in the recipe = 0.5 cups

Number of cups of resins in the recipe = 1 cup of resin

Therefore, 1 cup of resin is required for 0.5 cups of cranberries

2 × 1 = 2 cups of resins will be required for 2 × 0.5 = 1 cup of cranberries

4. The recipe will make ___ bags of snack mix if Sherry  uses only 1 cup of granola

3 cups of granola are required for 6 bags of snack mix

Therefore; 3/3 = 1 cup of granola will be required for 6/3 = 2 bags of the snack mix

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The null hypothesis is a common statistical theory that contends that there is no statistically significant association between any two sets of a single observed variable.

The hypothesis suggests no two given sets make any significance meaning until and unless they are proven wrong.

As given in the example,

The group of answer choices the (population) mean amount of time reading and sending e-mails daily is greater than 60 minutes and the (population) mean amount of time reading and sending e-mails daily is equal to 60 minutes.

You can see in one set the amount of reading and sending e-mails is more than 60 minutes and in other one the amount of time reading and sending e-mails is equal to 60 minutes which doesn't make any sense if you consider them both in a single set of information.

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It is the bottom left one

It is an absolute value graph, so the line should be a y = x graph but all y values are positive.

the bottom left one shows the same line with the y increased by 5

The right Riemann sum for arctan(1 + xdx) is Σ[arctan(1 + iΔx)]Δx, where i ranges from 1 to n and Δx is the width of each subinterval. The correct answer among the options provided is (arctan(1 + Δx) + arctan(1 + 2Δx) + ... + arctan(1 + nΔx))Δx.

In a right Riemann sum, the function is evaluated at the right endpoint of each subinterval. Therefore, we add up the values of arctan(1 + iΔx) at the endpoints of the subintervals, where i ranges from 1 to n. The width of each subinterval is Δx, so we multiply the sum by Δx to get the approximate value of the integral.

The provided expression (arctan(1 + Δx) + arctan(1 + 2Δx) + ... + arctan(1 + nΔx))Δx satisfies the conditions of a right Riemann sum, where the function is evaluated at the right endpoint of each subinterval. Therefore, this is the correct option among the given choices.

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The directional derivative of the function f(x, y, z) = xey + ye^z + zet at a given point in the direction of a vector v can be computed using the gradient of f and the dot product

Let's denote the given point as P(0, 0, 0) and the vector as v = ⟨a, b, c⟩. The gradient of f is given by ∇f = ⟨∂f/∂x, ∂f/∂y, ∂f/∂z⟩. To find the directional derivative, we evaluate the dot product between the gradient and the unit vector in the direction of v: D_vf(P) = ∇f(P) · (v/||v||) = ⟨∂f/∂x, ∂f/∂y, ∂f/∂z⟩ · ⟨a/√(a^2 + b^2 + c^2), b/√(a^2 + b^2 + c^2), c/√(a^2 + b^2 + c^2)⟩.

Now, we substitute the function f into the gradient expression and simplify the dot product. The resulting expression will give us the directional derivative of f at point P in the direction of vector v.

Please note that the second paragraph of the answer would involve the detailed calculations, which cannot be provided in this text-based format.

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The probability of selecting either 2 or 4 from the given sample space is 0.54, the probability of selecting either 1, 3, or 5 from the sample space is 0.46 and the probability of selecting a prime number from the given sample space is 0.43.

(a) To find the probability of {2, 4}, we need to add the individual probabilities of 2 and 4:

P({2, 4}) = P(2) + P(4) = 0.18 + 0.36 = 0.54

Therefore, the probability of selecting either 2 or 4 from the given sample space is 0.54.

(b) Similarly, to find the probability of {1, 3, 5}, we need to add the individual probabilities of 1, 3, and 5:

P({1, 3, 5}) = P(1) + P(3) + P(5) = 0.07 + 0.25 + 0.14 = 0.46

So, the probability of selecting either 1, 3, or 5 from the sample space is 0.46.

(c) To find the probability of selecting a prime number, we need to determine the probabilities of selecting the prime numbers in the sample space, which are 2 and 3:

P(prime) = P(2) + P(3) = 0.18 + 0.25 = 0.43

Therefore, the probability of selecting a prime number from the given sample space is 0.43.

Therefore, the probability of selecting either 2 or 4 from the given sample space is 0.54, the probability of selecting either 1, 3, or 5 from the sample space is 0.46 and the probability of selecting a prime number from the given sample space is 0.43.

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Incomplete question:

For the sample space {1, 2, 3, 4, 5} the following probabilities are assigned: P(1) = 0.07, P(2) = 0.18, P(3) = 0.25, P(4) = 0.36, and P(5) = 0.14.

(a) Find the probability of {2, 4}.

(b) Find the probability of {1, 3, 5}.

(c) Find the probability of selecting a prime.

Answer:

it is a

Step-by-step explanation:

I might not know but I guess the answer is D

1. The function for this problem is given as follows: f(x) = x - 3.

2. The numeric value of the function at x = 2 is of f(2) = -1.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

We define the function in this problem as follows:

f(x) = x - 3.

The numeric value at x = 2 is found replacing the lone instance of 2 by 2, hence:

f(2) = 2 - 3

f(2) = -1.

We attribute the function in this problem as f(x) = x - 3.

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Answer:

The answer is 8

Step-by-step explanation:

if you need proof do to desmos and type it in

Answer:

The product of the degree is

3/2 × 1/2

=3/4

16^3/4

=8 (which is)

\( \sqrt[4]{16 {}^{3} } \)

8 is the answer

Answer:

The slope is 30, and the y-intercept is 75.

Step-by-step explanation:

Use two points from the table, and find the equation of a line given two points.

Point 1: (1, 105)

Point 2: (3, 165)

y = mx + b

slope = m = (y_1 - y_1)/(x_2 - x_1)

m = (165 - 105)/(3 - 1) = 60/2 = 30

y = 30x + b

Use point (1, 105) for x and y.

105 = 30(1) + b

105 = 30 + b

b = 75

y = 30x + 75

The slope is 30, and the y-intercept is 75.

Answer:

the car is traveling at a mph of 65 per hour.

Step-by-step explanation:

hope this helped out in some way.